Digi camera video capture or camcorder video?
To add to Sean's good points about shallower DOF ability, etc., I would say, from reading way too much stuff regarding this, that the traditional dSLRs are somewhat behind the latest mirrorless.
I also have a GH3, and we all know that the new GH4 is stupendous in this area. I also have an RX10 which does very well compared to my GH3 and can even offer some shallow DOF if shot correctly. All three of these cameras (and the older GH2s) are optimized for video, and the newer ones, beginning with the GH3, are also very good at stills. Although I bought the RX10 for several reasons - they were all video-oriented reasons - I was pleasantly surprised at its stills level.
I suggest you read the reviews of the above models, and also any dSLRs you're looking at; serious reviews of the GH4 are surfacing now, on sites like this, YouTube, Vimeo, etc.
"Knowledge is good." Emil Faber